Simply supported beam

Mesh element size : 2mm

Result

Maximum Deformation along y axis = -20.035mm in the middle of the beam

Equivalent Von mises stress = 480.16Mpa (max) 0.2MPa (min)

link to images of analysis

Analytical solutions

Moment of inertia = 1/12 bh^3 (for rectangular cross-section)

= (1/12)*0.025*(0.025)^3

= 3.26 * 10^(-8) m^4

Shear force on the beam = f/2 = 5000N(magnitude)

Bending Moment on the beam = (f/2)*(l/2)= 5000N*0.5m

= 2500Nm

Maximum displacement = -f*l^3/(48EI) = -25.56 mm

Maximum Bending stress = (M*(h/2))/I = 958.58 MPa

Analytical Comparison between numerically and analytically obtained values

It is observed that the analytically calculated values for displacement are slightly greater than those obtained numerically from Ansys.

Ansys analyses the beam by evaluating stress and displacement at discrete mesh elements and then combines the data to yield the final result.

whereas the numerical methods used in general take into consideration infinitesmally small elements and the final result is then obtained by mathematical integration.

Hence by reducing the element size of the meshing we can obtain more accurate results which will be quite close to the theoretically calculated values.